Order algebras

• Autorzy: Chajda I. , Halaš R.
• Języki publikacji: EN

Abstrakty

EN

To every ordered set with a greatest element is assigned an order algebra, a Hilbert algebra occuring in intuicionistic logic. We prove some basic properties of order algebras and characterize their ideals and congruences. We introduce a concept of (relative) annihilator and show that it is a (relative) pseudocomplement in the lattice of all ideals.

Słowa kluczowe

EN

ordered set; order algebra; ideal; annihilator

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 1
• Strony: 1--10
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Chajda I.

• Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

autor

Halaš R.

• Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

Bibliografia

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• [3] D. Busenag, A note on deductive systems of Hilbert algebra, Kobe J. Math. 2 (1985), 29-35.
• [4] I. Chajda, Rees ideal algebras, Math. Bohem. 122 (1997), 125-130.
• [5] I. Chajda, R. Halas, Congruences and ideals in Hilbert algebras, Kyungpook Math. J. 39 (1999), 429-432.
• [6] A. Diego, Sur les algèbres de Hilbert, Collection de Logique Mathematique, Series A, (Ed. Hermann, Paris), 21 (1966), 1-52.
• [7] W. A. Dudek, On ideals in Hilbert algebras, Acta Univ. Palack. Olomouc, Mathematica 38 (1999), 31-34.
• [8] W. A. Dudek, R. Rousseau, Set-theoretic relations and BCH-algebras with trivial structure , Rev. Res. Fac. Sci. Novi Sad 25 (1995), 75-82.
• [9] A. Romanowska, T. Traczyk, On commutative BCK-algebras, Math. Japonica 25 (1980), 567-583.
• [10] A. Romanowska, T. Traczyk, Commutative BCK-algebras. Subdirectly irreducible algebras and varieties, Math. Japonica 27 (1981), 35-48.
• [11] R. T. Tichy, The Rees congruences in universal algebras, Publ. Inst. Math. (Beograd) 29 (1981), 229-239.